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Unformatted text preview: Endogeneity and Imperfect Instruments: Estimating Bounds for the Effect of Early Childbearing on High School Completion Steffen Reinhold * Tiemen Woutersen August 11, 2009 Abstract This paper derives informative bounds of the effect of early childbearing on high school completion. We allow the exclusion restriction of the instrument to be violated. In particu- lar, we assume that the correlation between the instrument and the structural error is smaller than the correlation between the structural error and the endogenous regressor. We derive a confidence interval using the regular bootstrap and find that the least squares estimate is outside this confidence interval. That is, the bias of the least squares estimator is both substantial and statistically significant. Keywords: Instrumental Variables, Validity, Identification, Bounds, Teenage Childbearing, Educational Attainment. JEL Classification: C310, J130 * Mannheim Research Institute for the Economics of Aging, University of Mannheim; L13,17; 68131 Mannheim; Germany; email: reinhold@mea.uni-mannheim.de Johns Hopkins University, Department of Economics; 3400 N. Charles Street; MD 21218; email: woutersen@jhu.edu. We would like to thank Colleen Carey, Norman Swanson, Roger Klein, and Anne Morrison Piehl for valuable comments. 1 1 Introduction There is a close association between early childbearing and adverse economic outcomes for mothers and their children such as poverty risk, lower educational achievement, and de- pressed earnings. While it is plausible to describe these outcomes as consequences of early fertility decisions, this correlation can also arise from a correlation of unobserved factors with early childbearing. Instrumental variables are one approach to deal with the problems of endogenous regressors. However, depending on the exact choice of the instruments, a wide range of estimates emerges. An instrument needs to be correlated with the endogenous regressor teenage childbearing (relevance) but it must not be correlated with the structural error term in the outcome equa- tion (validity). One problem with this approach is that often doubts linger as to whether the instruments satisfy this second assumption. In this paper, we employ a novel set identi- fication approach with imperfect instruments based on the assumption that the correlation between the instrument and the structural error is smaller than the correlation between the structural error and the endogenous regressor, childbearing. Nevo and Rosen (2008) were the first to use this inequality. This approach relaxes the validity assumption, allowing limited correlation with the error term and thus widens the set of potential instruments. Nevo and Rosens work builds on a recent literature on partial identification. Horowitz and Manski (1998) develop interval estimates that asymptotically cover the entire identified region with fixed probability. Chernozhukov, Hong and Tamer (2007) extend this approach through formulating the problem of covering the entire identified region as a minimization problem.formulating the problem of covering the entire identified region as a minimization problem....
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